That's completely false actually. He wrote the poem comparing italy and france (italy being the poem my last duchess and france being the poem Count Gismond) and how corrupt both countries where. My last duchess has to do wit the duke of italy at the time (in real life) and how his wife was a very personable women who was admired and admired many. She was kinda and caring but the duke became jealous and too proud. He sensed that she did not value "his gift of a nine hundred years name" and since he assumed she was unfaithful had her killed even though there is no evidence of her infidelity. This has nothing to do with Brownings wife Elizabeth. The duke is actually an objective man stricken by pride and selfishness. Since he couldnt have her all to himself no one would have her, which is why he hides the painting behind a curtain so only he can draw the curtain away to see her painting.